Question: There are 5 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Solution: Given 5 people, each person shakes the hands of 4 other people. The following is almost the answer. $5 \times 4 = 20$ We have double counted the handshakes though, since Luis shaking Christopher's hand is the same handshake as Christopher shaking Luis's hand. Therefore, the following is the correct answer. $\dfrac{5 \times 4}{2} = 10$